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Spatial organization, predictability, and determinism in ventricular fibrillation. (English) Zbl 1069.92510
Summary: The degree of spatial organization of ventricular fibrillation (VF) is a fundamental dynamical property of arrhythmia and may determine the success of proposed therapeutic approaches. Spatial organization is closely related to the dimension of VF, and hence to its predictability and controllability. We have explored several techniques to quantify spatial organization during VF, to predict patterns of activity, and to see how spatial organization and predictability change as the arrhythmia progresses. Epicardial electrograms recorded from pig hearts using rectangular arrays of unipolar extracellular electrodes (1 mm spacing) were analyzed. The correlation length of VF, the number of Karhunen-Loève modes required to approximate data during VF, the number, size and recurrence of wavefronts, and the mean square error of epicardial potential fields predicted 0.256 seconds into the future were all estimated. The ability of regularly-timed pacing stimuli to capture areas of fibrillating myocardium during VF was confirmed by a significant increase in local spatial organization. Results indicate that VF is neither “low-dimensional chaos” \((\text{dimension} < 5)\) nor “random” behavior \((\text{dimension} =\infty )\), but is a high-dimensional response with a degree of spatial coherence that changes as the arrhythmia progresses.

MSC:
92C50 Medical applications (general)
92C55 Biomedical imaging and signal processing
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References:
[1] DOI: 10.1161/01.CIR.51.5.761 · doi:10.1161/01.CIR.51.5.761
[2] DOI: 10.1016/0002-8703(64)90371-0 · doi:10.1016/0002-8703(64)90371-0
[3] DOI: 10.1063/1.166297 · doi:10.1063/1.166297
[4] DOI: 10.1161/01.RES.77.4.849 · doi:10.1161/01.RES.77.4.849
[5] DOI: 10.1126/science.1519060 · doi:10.1126/science.1519060
[6] DOI: 10.1098/rstb.1985.0001 · doi:10.1098/rstb.1985.0001
[7] DOI: 10.1016/0022-460X(92)90419-X · doi:10.1016/0022-460X(92)90419-X
[8] DOI: 10.1103/PhysRevLett.59.845 · doi:10.1103/PhysRevLett.59.845
[9] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[10] DOI: 10.1103/PhysRevLett.65.3211 · doi:10.1103/PhysRevLett.65.3211
[11] DOI: 10.1038/369129a0 · doi:10.1038/369129a0
[12] DOI: 10.1142/S0218127491000403 · Zbl 0874.58029 · doi:10.1142/S0218127491000403
[13] Johnson E., J. Am. College of Cardiology 19 pp 90A– (1992)
[14] DOI: 10.1161/01.CIR.86.1.331 · doi:10.1161/01.CIR.86.1.331
[15] Rogers J., Ann. Biomed. Eng. 25 pp 748– (1997)
[16] DOI: 10.1007/BF02684160 · doi:10.1007/BF02684160
[17] DOI: 10.1103/PhysRevE.47.R780 · doi:10.1103/PhysRevE.47.R780
[18] DOI: 10.1103/PhysRevLett.62.422 · doi:10.1103/PhysRevLett.62.422
[19] DOI: 10.1103/PhysRevLett.62.1619 · doi:10.1103/PhysRevLett.62.1619
[20] DOI: 10.1016/0167-2789(91)90194-E · doi:10.1016/0167-2789(91)90194-E
[21] DOI: 10.1016/0167-2789(89)90123-1 · doi:10.1016/0167-2789(89)90123-1
[22] DOI: 10.1146/annurev.fl.25.010193.002543 · doi:10.1146/annurev.fl.25.010193.002543
[23] DOI: 10.1161/01.CIR.92.3.535 · doi:10.1161/01.CIR.92.3.535
[24] DOI: 10.1109/10.391158 · doi:10.1109/10.391158
[25] DOI: 10.1006/cbmr.1994.1019 · doi:10.1006/cbmr.1994.1019
[26] DOI: 10.1161/01.RES.68.5.1204 · doi:10.1161/01.RES.68.5.1204
[27] DOI: 10.1111/j.1749-6632.1990.tb15091.x · doi:10.1111/j.1749-6632.1990.tb15091.x
[28] DOI: 10.1109/10.412656 · doi:10.1109/10.412656
[29] DOI: 10.1109/TBME.1971.4502813 · doi:10.1109/TBME.1971.4502813
[30] DOI: 10.1161/01.RES.49.1.186 · doi:10.1161/01.RES.49.1.186
[31] DOI: 10.1209/0295-5075/14/4/003 · doi:10.1209/0295-5075/14/4/003
[32] DOI: 10.1126/science.270.5239.1222 · doi:10.1126/science.270.5239.1222
[33] DOI: 10.1016/0167-2789(89)90074-2 · Zbl 0671.62099 · doi:10.1016/0167-2789(89)90074-2
[34] DOI: 10.1038/344734a0 · doi:10.1038/344734a0
[35] DOI: 10.1161/01.RES.67.4.886 · doi:10.1161/01.RES.67.4.886
[36] DOI: 10.1016/0167-2789(95)00025-Y · doi:10.1016/0167-2789(95)00025-Y
[37] DOI: 10.1016/S0002-8703(40)90874-2 · doi:10.1016/S0002-8703(40)90874-2
[38] DOI: 10.1161/01.RES.74.6.1071 · doi:10.1161/01.RES.74.6.1071
[39] DOI: 10.1103/PhysRevLett.78.1687 · doi:10.1103/PhysRevLett.78.1687
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